If the second term in an arithmatic sequence is 4, and the tenth term is 15, what is the first term in the sequence?
To find the first term (a) of an arithmetic sequence, you can use the formula:
a_n = a + (n - 1)d
Where:
- a_n is the nth term in the sequence.
- a is the first term.
- n is the term number.
- d is the common difference between terms.
In this case, you know that the second term (a_2) is 4, and the tenth term (a_10) is 15. So, you have:
a_2 = a + (2 - 1)d = a + d = 4 a_10 = a + (10 - 1)d = a + 9d = 15
Now, you have a system of two equations with two unknowns:
- a + d = 4
- a + 9d = 15
You can subtract equation 1 from equation 2 to eliminate "a":
(a + 9d) - (a + d) = 15 - 4
This simplifies to:
8d = 11
Now, divide both sides by 8 to solve for "d":
d = 11 / 8 = 1.375
Now that you have the value of "d," you can substitute it back into equation 1 to find "a":
a + 1.375 = 4
Subtract 1.375 from both sides:
a = 4 - 1.375 = 2.625
So, the first term in the arithmetic sequence is approximately 2.625, which is equivalent to 2.63 when rounded to two decimal places. Therefore, the answer is 2.63.
Related Question
View MorePromotion
Download Our Mobile Apps
